feat(search): hybrid semantic search via RRF fusion (RECOMMENDATIONS #4b)

The flagship slice (docs/discovery/05): when a free-text query runs and embeddings
are available, fuse lexical top-50 (ts_rank_cd) with vector top-50 (pgvector cosine
over the structured-filtered set) using Reciprocal Rank Fusion. Placed BEFORE the
fuzzy fallback so queries with ZERO lexical hits still get semantic recall — found
and fixed during review (the fuzzy path would otherwise swallow pure-semantic
queries). Exact lexical hits keep winning (rank in both lists); deeper pages fall
through to lexical paging; ANY failure (Ollama down, nothing embedded) silently
degrades to the lexical/fuzzy path — AI can never break search.

LiveDb test proves the recall win: a 'banana' query surfaces an email with no
keyword overlap, ranked first, against real pgvector. 5 LiveDb + full suite green;
format clean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/InboxIntel.Infrastructure/Search/SearchService.cs

@@ -5,6 +5,7 @@ using InboxIntel.Domain.Entities;
 using InboxIntel.Domain.Enums;
 using InboxIntel.Infrastructure.Persistence;
 using Microsoft.EntityFrameworkCore;
+using Pgvector.EntityFrameworkCore;
 
 namespace InboxIntel.Infrastructure.Search;
 
@@ -18,7 +19,13 @@ namespace InboxIntel.Infrastructure.Search;
 public class SearchService : ISearchService
 {
     private readonly AppDbContext _db;
-    public SearchService(AppDbContext db) => _db = db;
+    private readonly IEmbeddingProvider? _embeddings;
+
+    public SearchService(AppDbContext db, IEmbeddingProvider? embeddings = null)
+    {
+        _db = db;
+        _embeddings = embeddings;
+    }
 
     public async Task<PagedResult<EmailSummaryDto>> SearchAsync(Guid userId, SearchRequestDto r, CancellationToken ct = default)
     {
@@ -73,6 +80,18 @@ public class SearchService : ISearchService
 
         var total = await matched.CountAsync(ct);
 
+        // Hybrid semantic fusion (docs/discovery/05): when embeddings are available, fuse
+        // lexical top-K with vector top-K via Reciprocal Rank Fusion. Runs BEFORE the fuzzy
+        // fallback so a query with ZERO lexical hits (pure semantic recall — "gym receipt"
+        // phrased differently) still surfaces results. Exact lexical hits keep winning (they
+        // rank in both lists). Deeper pages fall through to lexical paging; any failure
+        // (Ollama down, nothing embedded yet) silently degrades to the lexical/fuzzy path.
+        if (hasFreeTextQuery && _embeddings is { IsAvailable: true })
+        {
+            var hybrid = await TryHybridAsync(structured, matched, term, total, r, ct);
+            if (hybrid is not null) return hybrid;
+        }
+
         // Fuzzy/typo fallback: ONLY when a free-text search found nothing exact. word_similarity
         // with an explicit 0.3 threshold — pg_trgm's default 0.6 misses real typos
         // ("recieved" -> "received" scores ~0.39). Rare path, so the (non-indexed) scan over the
@@ -137,4 +156,73 @@ public class SearchService : ISearchService
             TotalCount = total
         };
     }
+
+    private const int HybridK = 50;      // candidates taken from each layer
+    private const int RrfConstant = 60;  // standard RRF dampening constant
+
+    /// <summary>
+    /// RRF fusion of lexical and vector candidates. Returns null when the requested page
+    /// lies beyond the fused window or anything fails — caller falls back to lexical.
+    /// </summary>
+    private async Task<PagedResult<EmailSummaryDto>?> TryHybridAsync(
+        IQueryable<Email> structured, IQueryable<Email> lexical, string term, int lexicalTotal,
+        SearchRequestDto r, CancellationToken ct)
+    {
+        try
+        {
+            var lexIds = await lexical
+                .OrderByDescending(e => e.SearchVector!.RankCoverDensity(EF.Functions.WebSearchToTsQuery("english", term)))
+                .ThenByDescending(e => e.SentAtUtc)
+                .Take(HybridK).Select(e => e.Id).ToListAsync(ct);
+
+            var queryVec = await _embeddings!.EmbedAsync(term, ct);
+            List<Guid> vecIds = new();
+            if (queryVec.Length > 0)
+            {
+                var qv = new Pgvector.Vector(queryVec);
+                vecIds = await structured
+                    .Where(e => e.Embedding != null)
+                    .OrderBy(e => e.Embedding!.CosineDistance(qv))
+                    .Take(HybridK).Select(e => e.Id).ToListAsync(ct);
+            }
+            if (vecIds.Count == 0) return null; // nothing embedded yet → lexical path
+
+            var scores = new Dictionary<Guid, double>();
+            for (var i = 0; i < lexIds.Count; i++)
+                scores[lexIds[i]] = scores.GetValueOrDefault(lexIds[i]) + 1.0 / (RrfConstant + i + 1);
+            for (var i = 0; i < vecIds.Count; i++)
+                scores[vecIds[i]] = scores.GetValueOrDefault(vecIds[i]) + 1.0 / (RrfConstant + i + 1);
+
+            var fused = scores.OrderByDescending(kv => kv.Value).Select(kv => kv.Key).ToList();
+            var pageIds = fused.Skip((r.Page - 1) * r.PageSize).Take(r.PageSize).ToList();
+            if (pageIds.Count == 0 && r.Page > 1) return null; // deep page → lexical paging
+
+            var headlineOpts =
+                $"StartSel={(char)0xE000},StopSel={(char)0xE001},MaxWords=16,MinWords=5,ShortWord=2,HighlightAll=false";
+            var rows = await _db.Emails.AsNoTracking()
+                .Where(e => pageIds.Contains(e.Id))
+                .Select(e => new EmailSummaryDto(
+                    e.Id, e.GmailMessageId, e.Subject, e.Snippet,
+                    e.Sender!.Address, e.Sender.DisplayName, e.SentAtUtc,
+                    e.IsUnread, e.IsStarred, e.HasAttachments, e.SizeEstimateBytes, e.Category,
+                    e.HasListUnsubscribe, e.SupportsOneClickUnsubscribe,
+                    EF.Functions.WebSearchToTsQuery("english", term).GetResultHeadline("english", e.BodyText ?? "", headlineOpts)))
+                .ToListAsync(ct);
+            var byId = rows.ToDictionary(x => x.Id);
+            var items = pageIds.Where(byId.ContainsKey).Select(id => byId[id]).ToList();
+
+            return new PagedResult<EmailSummaryDto>
+            {
+                Items = items,
+                Page = r.Page,
+                PageSize = r.PageSize,
+                // Semantic recall can exceed the lexical match count.
+                TotalCount = Math.Max(lexicalTotal, fused.Count)
+            };
+        }
+        catch
+        {
+            return null; // AI must never break search — degrade to lexical
+        }
+    }
 }

tests/InboxIntel.IntegrationTests/LiveDbSearchTests.cs

@@ -123,4 +123,54 @@ public class LiveDbSearchTests
         }
         finally { await CleanupAsync(opts, uid); }
     }
+
+    private sealed class DirectionalFakeEmbeddings : IEmbeddingProvider
+    {
+        public bool IsAvailable => true;
+        public Task<float[]> EmbedAsync(string text, CancellationToken ct = default)
+        {
+            // Deterministic "semantics": anything fruit-flavoured points one way, else the other.
+            var v = new float[768];
+            if (text.Contains("banana") || text.Contains("tropical")) v[0] = 1; else v[1] = 1;
+            return Task.FromResult(v);
+        }
+        public async Task<IReadOnlyList<float[]>> EmbedBatchAsync(IReadOnlyList<string> texts, CancellationToken ct = default)
+        {
+            var list = new List<float[]>();
+            foreach (var t in texts) list.Add(await EmbedAsync(t, ct));
+            return list;
+        }
+    }
+
+    [Fact]
+    public async Task Hybrid_search_surfaces_semantic_match_with_zero_keyword_overlap()
+    {
+        if (Conn is null) return;
+        var opts = Options();
+        var uid = await SeedAsync(opts);
+        try
+        {
+            var embeddings = new DirectionalFakeEmbeddings();
+            using (var prep = new AppDbContext(opts, new FakeCurrentUser()))
+            {
+                // "Weekly notes" gets a fruit-direction embedding (semantically related to the
+                // query); "Invoice March" points elsewhere. Neither subject contains "banana".
+                var near = await prep.Emails.FirstAsync(e => e.UserId == uid && e.Subject == "Weekly notes");
+                near.Embedding = new Vector(await embeddings.EmbedAsync("tropical"));
+                var far = await prep.Emails.FirstAsync(e => e.UserId == uid && e.Subject == "Invoice March");
+                far.Embedding = new Vector(await embeddings.EmbedAsync("finance"));
+                await prep.SaveChangesAsync();
+            }
+
+            using var ctx = new AppDbContext(opts, new FakeCurrentUser { UserId = uid });
+            var res = await new SearchService(ctx, embeddings)
+                .SearchAsync(uid, GmailQueryParser.Parse("banana", 1, 10));
+
+            // Zero lexical hits for "banana" — hybrid must still surface the semantically
+            // nearest email, ranked first.
+            res.Items.Should().NotBeEmpty("semantic recall should fire with zero keyword overlap");
+            res.Items[0].Subject.Should().Be("Weekly notes");
+        }
+        finally { await CleanupAsync(opts, uid); }
+    }
 }